Engler — Figurate Numhers. 



41 



Continuing this process precisely as before for the series 

 1, 4, 10, . . . 



84 

 84 



84 

 84 

 84 

 84 



Table 4. 



we obtain as the formula 



n{n-^l){n-\-2){n+Z){n+4. ) 

 ^ 1-2-3-4-5 



for the sum of the series 1, 5, 15, 35, 70, 126, 210 



From 



(5) 



15 35 70 126 



1 5 15 35 70 fl26 

 126 



126 

 126 

 126 

 Table 5 



210 

 210 

 210 

 210 

 210 

 210 



we obtain as formula 



njn^l) (n+2) (l^+3)(l^+4) (^^+5) 

 ^ l'2-3-4-5-6 



for the sum of the series 1, 6, 21, 56, 126, 252 



(6) 



